$\backslash$table$[[,\backslash$table$[[$Number of$],[$Fans$]],\backslash$table$[[$Number of$],[$Cooling Coils$]],\backslash$table$[[$Manufacturing$],[$Time $($hours$)]]],[$Economy$,1,1,8],[$Standard$,1,2,12],[$Deluxe$,1,4,14]]$

For the coming production period, the company has $220$ fan motors, $340$ cooling coils, and $2,600$ hours of manufacturing time available. How many economy models $(E),$ standard models $(S),$ and deluxe models $(D)$ should the company produce in order to maximize profit? The linear programming model for the problem is as follows:

Max $63E+95S+135D$

$s.t.$

$1E+1S+1D220$ Fan motors

$1E+2S+4D340$ Cooling coils

$8E+12S+14D2,600$ Manufacturing time

The computer solution is shown below.

Optimal Objective Value $=17700\mathrm{.}00000$

$\backslash$table$[[$Variable$,$Value,Reduced Cost$],[$E$,100\mathrm{.}00000,0\mathrm{.}00000],[$S$,120\mathrm{.}00000,0\mathrm{.}00000],[$D$,0\mathrm{.}00000,-24\mathrm{.}00000],[,,],[$Constraint$,$Slack$/$Surplus$,$Dual Value$],[1,0\mathrm{.}00000,31\mathrm{.}00000],[2,0\mathrm{.}00000,32\mathrm{.}00000],[3,360\mathrm{.}00000,0\mathrm{.}00000]]$

$\backslash$table$[[$Variable$,\backslash$table$[[$Objective$],[$Coefficient$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[$E$,63\mathrm{.}00000,12\mathrm{.}00000,15\mathrm{.}50000],[$S$,95\mathrm{.}00000,31\mathrm{.}00000,8\mathrm{.}00000],[$D$,135\mathrm{.}00000,24\mathrm{.}00000,$Infinite$]]$

$\backslash$table$[[$Constraint$,\backslash$table$[[$RHS$],[$Value$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[1,220\mathrm{.}00000,90\mathrm{.}00000,50\mathrm{.}00000],[2,340\mathrm{.}00000,90\mathrm{.}00000,120\mathrm{.}00000],[3,2600\mathrm{.}00000,$Infinite,$360\mathrm{.}00000]]$

$($A$)$ identify the range of optimality for each objective function coefficient. $($IF THERE ARE NO UPPER OR LOWER LIMIT, ENTER NO LIMIT$)$

E blank to blank

S blank to blank

D blank to blank

$($B$)$ suppose the profit for the economy model is increased by $$6$ per unit, the profit for the standard model is decreased by $$2$ per unit, and the profit for the deluxe model is increased by $$4$ per unit. What will be the new optimal solution be$?$

E blank units

S blank units

D blank units

$($c$)$ identify the range of feasibility for the right$-$hand$-$side values. $($If no limit enter, no limit$)$

Constraint $1$ blank to blank

Constraint $2$ blank to blank

Constraint $3$ blank to blank

$($D$)$ if the number of fan motors avaliable for production is increased by $120,$ will the dual value for the constraint change? Explain

Yes, the dual value will change because because $120$ is greater than

the allowable increase of $90.$

Yes, the dual value will change becase $120$ is greater than the allowable increase of $12$

No$,$ the dual value will not change because $120$ is less than the allowable increase of $310$

No$,$ the dual value will not change because there is no upper limit to how much the constraint can increase.

Answer A through D based upon the photo provided